The decorator pattern allows you to add behaviour dynamically at runtime to an instance of a particular class, whereas inheritance adds behaviour at compile time.
You can make use of inheritance when applying the decorator pattern, although that's not always a necessity.
So it's perfectly ok to use both inheritance and composition when creating a decorator class, if you don't have a common interface you can implement.
Or if you want to create an (abstract) "base" decorator class.

Build a man a fire, and he'll be warm for a day. Set a man on fire, and he'll be warm for the rest of his life.